How to insert key to a constrained bone with "child of"
The "Child Of" constraint is a tricky one to get right. I would recommend using multiple parent objects, and adding a "Child Of" constraint for each parent.


Create a parent empty on the ground at the "pick up" location.
Create a parent empty on the ground at the "put down" location.
Create a parent empty that you parent to the hand bone.
Create three "Child Of" constraints, one for each parent empty.


Now you can animate the influence of each constraint. When the sword should be at the "pick up" location, that constraint has an influence of 100%. When the sword is picked up, the "hand bone" constraint gets 100% influence. When the sword is put down, the "put down" contstraint gets 100% influence.